Base field: \(\Q(\sqrt{-111}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 28\); class number \(8\).
Form
| Weight: | 2 | |
| Level: | 23.2 = \( \left(23, a + 12\right) \) | |
| Level norm: | 23 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.111.1-23.2 (dimension 2) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.111.1-23.2-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 23 \) | 23.2 = \( \left(23, a + 12\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 100 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( 0 \) |
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( 0 \) |
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( -1 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 1\right) \) | \( 0 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( -4 \) |
| \( 7 \) | 7.1 = \( \left(7, a\right) \) | \( 1 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 6\right) \) | \( -3 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 2\right) \) | \( 4 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 14\right) \) | \( 4 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 10\right) \) | \( -4 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 5\right) \) | \( -8 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 23\right) \) | \( -4 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 18\right) \) | \( -6 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 9\right) \) | \( 0 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 49\right) \) | \( -12 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 15\right) \) | \( 0 \) |
| \( 67 \) | 67.2 = \( \left(67, a + 51\right) \) | \( -8 \) |
| \( 73 \) | 73.1 = \( \left(73, a + 26\right) \) | \( 11 \) |
| \( 73 \) | 73.2 = \( \left(73, a + 46\right) \) | \( -13 \) |
| \( 89 \) | 89.1 = \( \left(89, a + 22\right) \) | \( 0 \) |